Chapter 8: Right Triangles and Trigonometry¶
8.1: Geometric Mean¶
Vocab
The geometric mean is \(\sqrt{a+b}\) or \(\sqrt[3]{a+b+c}\).
TODO: Part 2 of the lesson
8.2: The Pythagorean Theorem and Its Converse¶
Vocab
A hypotenuse is the longest side of a right triangle.
Pythagorean theorem states that \(a^2 + b^2 = c^2\) (\(\sqrt{a^2+b^2}\) ) where a and b represent the two legs of a right triangle and c represent the hypotenuse of the triangle.
The converse of the pythagorean theorem states that when provided with all the sides of a triangle \(a^2 + b^2 = c^2\), c representing the longest side, is true, then the triangle is right.
Pythagorean Inequality Theorems
Inequality |
\(a^2 + b^2 > c^2\) |
\(a^2 + b^2 = c^2\) |
\(a^2 + b^2 < c^2\) |
|---|---|---|---|
Type |
Acute |
Right |
Obtuse |
TODO: Prove pythagorean theorem.